For encoding an image, it is well known in the art to transform image blocks of the image using discrete cosine transforms (DCT) or discrete wavelet transform (DWT).
For instance, DCT is commonly used in hybrid video coding framework to exploit redundancy in spatial domain and exhibit excellent energy compaction for highly correlated signals, as well as the properties of being separable, symmetric and orthogonal.
Current image/video coding standards usually use 2 Dimensional separable DCT or DWT for coding, whose basis functions can be generated by multiplying the horizontally oriented 1-D basis functions with vertically oriented set of the same functions.
For instance, for an exemplary N×N block firstly N N-point 1-D DCT operations (first 1-D transform) are performed vertically over the original pixels, to generate N×N intermediate coefficients; secondly N N-point 1-D DCT operations (second 1-D transform) are performed horizontally over the intermediate coefficients, to generate yet further transformed coefficients. This kind of scheme tends to do well for image texture details oriented strictly horizontally and vertically, while ringing artifacts tend to appear around other edge orientations, which significantly deteriorates the visual quality.
This problem is identified and addressed by C. L. Chang and B. Girod in “Directional-Adaptive Partitioned Block Transform for Image Coding”, ICIP 2008. Within this paper, the authors propose direction-adaptive partitioned block transform (DA-PBT) according to which the image block is divided into directional partitions with the partition boundaries aligned with direction of the first 1-D transform and with the length of the second 1-D transforms being limited such that they do not extend across partition boundaries. This ensures that the maximum required length of 1-D transforms equals N.